On the Eulerian formulation of a stress induced platelet activation function

The platelet phase, the second stage of hemostasis, commences around 15-20 seconds after an injury. It follows and overlaps with the vascular phase, during which blood vessels constrict to minimize blood loss.
As the injured blood vessel contracts, endothelial cells undergo contraction, revealing collagen fibers in the basement membrane and underlying connective tissue. Furthermore, the plasma membrane of endothelial cells becomes adhesive, preparing the site for platelet adhesion. Platelets...

The cell fragments known as platelets are disc-shaped, with an average diameter of about 3 μm and a thickness of roughly 1 μm. They play a crucial role in the body's vascular clotting system, which also involves plasma proteins, blood cells, and blood vessel tissues.
Platelets are continually replenished, circulating in the bloodstream for 9-12 days before being removed by phagocytes, primarily in the spleen. A microliter of circulating blood contains between 150,000 and 450,000...

When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...

The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress...

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...

The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...